Turbine with unevenly loaded rotor blades

ABSTRACT

An unevenly loaded turbine rotor blade is disclosed herein, the blade including a power-extracting region adapted for radially-varied (relative to the axis of rotation) power extraction per mass flow rate. The pitch and/or shape of the airfoil at a first radial position may be configured, so that power extraction per mass flow rate at the first radial position is different than power extraction per mass flow rate at a second radial position. Thus, the power-extracting region may be advantageously configured to take advantage of a non-uniform flow profile across a rotor plane such as may be induced using a shrouded turbine.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional Application Ser.No. 61/490,841, filed May 27, 2011, the entirety of which isincorporated by reference herein.

TECHNICAL FIELD

The present disclosure relates to turbine rotor blades of a particularstructure, and to shrouded turbines incorporating such blades. Morespecifically, the present rotor blade design comprises uneven loading(also known as “asymmetrical loading” or “unbalanced loading”).

BACKGROUND

Horizontal axis turbines (HAWTs) typically include two to five bladedrotors joined at a central hub. A conventional HAWT blade is commonlydesigned to provide substantially even blade loading across apower-extracting region of the blade. One common mathematical tool forpredicting and evaluating blade performance is blade element theory(BET). BET treats a blade as a set of component elements (also known as“stations”). Each component element may be defined by a radial crosssection of the blade (known as an airfoil) at a radial position (r)relative to the axis of rotation and width of the element (dr). ApplyingBET analysis, even blade loading may be characterized as each componentelement of the blade along the power-extracting region having a samepressure differential (Δp) during operation. Note that Δp/ρ=P/{dot over(m)}, wherein ρ is fluid density, P is power and in is mass flow rate.Given that fluid density is typically constant, pressure differentialmay be assumed proportional to power over mass flow rate. Thus, evenblade loading may also typically be characterized as each componentelement of the blade along the power-extracting region exhibiting a samepower extracted per mass flow rate. Note that a conventional HAWT blademay also include one or more non-power-extracting regions. For example,conventional HAWT blades are often tapered at the tip and/or root of theblade, for example, to reduce vortices. Such tapered regions orotherwise minimally loaded regions proximal to the tip and/or root ofthe blade are considered non-power-extracting regions for the purposesof the present disclosure.

Stations are typically designed/configured so as to maximize powerextraction across the blade while maintaining a constant power extractedper mass flow rate. Mass flow rate is defined as {dot over (m)}=ρνA,wherein ρ is fluid density, ν is flow velocity and A is the flow area(the “rotor swept area”). Flow area for each station may be calculatedas A=2πrdr. Note that station flow area increases as a function ofradial position impacting mass flow rate. Thus, the airfoil for eachstation is typically designed to maintain even loading while accountingfor different mass flow rates. Parameters which may be adjusted toensure even loading for different mass flow rates include pitch (alsoknown as the “angle of attack”) and/or airfoil shape, for example,characterized by chord length, maximum thickness (sometimes expressed asa percentage of cord length), mean camber line, and/or the like.Airfoils for a conventional evenly loaded HAWT blade typically exhibitlonger chord lengths and greater pitch toward the root than toward thetip to account for a higher mass flow rate toward the tip (note that forconventional unshrouded HAWTs, there is little difference between fluidvelocity at the center of the rotor plane and fluid velocity at theperimeter of the rotor plane.

Recent development efforts have seen the implementation of shroudedturbines, for example, to reduce the affect of fringe vortices and/or toincrease fluid flow velocity. One example of a shrouded mixer-ejectorwind turbine has been described in U.S. patent application Ser. No.12/054,050, which issued as U.S. Pat. No. 8,021,100 and is incorporatedherein in its entirety. Development of shrouded turbines for powerextraction is still in its infancy. Thus, there is a need for new andimproved blades designed and optimized to work within a shrouded turbineenvironment. These and other needs are addressed by way of the presentdisclosure.

BRIEF DESCRIPTION

The present disclosure relates to novel turbine blade designscharacterized by uneven blade loading. The present disclosure furtherrelates to systems and methods for utilizing and methods formanufacturing unevenly loaded turbine blades. Uneven blade loadingteaches away from the norm of the industry and is particularly usefulfor taking advantage of non-uniform flow profiles, e.g. such as may becreated by a shroud. Indeed, as recognized herein unevenly loaded bladesmay provide particular advantages, for example, greater power extractionand/or greater efficiency relative to conventional evenly loaded bladesparticularly in a shrouded turbine environment or in other turbineenvironments where fluid flow velocity is non uniform across the rotorplane.

An embodiment includes a shrouded axial flow fluid turbine including anaerodynamically contoured turbine shroud having an inlet and configuredto produce a non-uniform fluid velocity profile across a rotor planewhen exposed to a fluid flow. The fluid turbine also includes a rotordisposed downstream of the inlet and configured to extract energy fromfluid passing through the rotor plane. The rotor includes a central huband a plurality of blades, with each blade including a root regionhaving a blade root, a tip region having a blade tip, a mid-regiondisposed between the root region and the tip region, and a blade axisextending radially from the blade root to the blade tip. Each blade isconfigured to have a value of power extraction per mass flow rate at aradial position along the blade axis that is greater at a first radiusin the tip region of the blade than at second radius in the mid-regionof the blade when exposed to the non-uniform fluid velocity profile.

Another embodiment includes a rotor configured for use with a shroudedfluid turbine having a turbine shroud that creates a non-uniform fluidvelocity profile across a rotor plane when exposed to a fluid flow. Therotor includes a central hub with a central axis of rotation and one ormore rotor blades. Each each of the one or more rotor blades includes aroot region having a blade root that couples with the central hub, a tipregion having a blade tip, a mid-region disposed between the root regionand the tip region, and a blade axis extending from the blade root tothe blade tip. For each of the one or more rotor blades, a pitch of theblade as a function of radial position along the blade axis isconfigured to, when connected with the central hub, produce a powerextraction per mass flow rate that is greater at a first radius in thetip region of the blade than at second radius in the mid-region of theblade when exposed to the non-uniform fluid velocity profile.

An embodiment includes a method of operating a shrouded axial flow fluidturbine including an aerodynamically contoured turbine shroud having aninlet, and a rotor disposed downstream of the turbine shroud inlet. Therotor includes a plurality of blades with each blade having a rootregion including a blade root, a tip region including a blade tip, and amid-region disposed between the root region and the tip region. Themethod includes establishing a non-uniform fluid flow through a rotorplane in which an average velocity of fluid flowing through an area ofthe rotor plane associated with the tip region of each blade is greaterthan an average velocity of fluid flowing through an area of the rotorplane associated with the mid-region of each blade. The method alsoincludes extracting power from the non-uniform fluid flow using theplurality of blades by extracting a greater average power per mass flowrate over the tip region of each blade than an average power per massflow rate extracted over the a mid-region of each blade.

In an example embodiment, an unevenly loaded turbine blade is disclosed,the blade including a power-extracting region adapted forradially-varied (relative to the axis of rotation) power extraction permass flow rate. More particularly, the pitch and/or shape of the airfoilat a first radial position may be configured, so that the powerextraction per mass flow rate of the blade at the first radial positionis different than the power extraction per mass flow rate of the bladeat a second radial position. In one example embodiment, thepower-extracting region may be configured to take advantage of anon-uniform flow profile, for example, a flow profile where flowvelocity is expected to be greater at a first radial position than at asecond radial position. Thus, the power-extracting region may beconfigured such that power extraction per mass flow rate at the firstradial position is greater than power extraction per mass flow rate atthe second radial position. In one embodiment, the power-extractingregion may optimized for an expected relative flow velocity betweenfluid flow at a first radial position and fluid flow at a second radialposition. For example, the power-extracting region may optimized basedon optimal lift/drag ratios for each radial position such as a maximallift/drag ratio prior to stall or prior to a selected safety threshold.Thus, the greater the flow velocity at a radial position, the greaterthe optimal lift/drag ratio at that position and the greater the powerextraction per mass flow rate at that position. In an exampleembodiment, relative flow velocity between two radial positions may berelated, for example, proportional to relative power extraction per massflow rate between the two radial positions.

Another example embodiment relates in general to turbine environmentswherein fluid flow velocity is non-uniform across the rotor plane. Forexample, a turbine may include at least one shroud that is in closeproximity to or surrounds at least a portion of a rotor and affects anon-uniform flow profile. One skilled in the art will readily recognizethat the unevenly loaded rotor blades as taught herein may be employedin conjunction with numerous turbines that are, at least in part,shrouded.

One suitable example of a shrouded turbine is a mixer-ejector turbine inwhich an ejector shroud may be in close proximity to or surround an exitof a turbine shroud. It will be appreciated that embodiments of unevenlyloaded blades as described herein may be incorporated into to the designof the rotor of the mixer-ejector turbine. In one example embodiment,the turbine shroud may include a set of mixing lobes along the trailingedge that are in fluid communication with the inlet of the ejectorshroud. Together, the mixer lobes and the ejector shroud may form amixer-ejector pump that provides a means of energizing the wake behindthe rotor plane. The mixer-ejector pump may further provides increasedfluid velocity near the inlet of the turbine shroud, at the crosssectional area of the perimeter of the rotor plane.

The power coefficient of the mixer-ejector wind turbine may be betweenapproximately 1.2 and 2.0. The power output is derived from the ratedfluid velocity and rotor area and results in a given average totalpressure drop across the rotor plane. The total pressure is representedby:

${\Delta \; P_{T}} = \frac{{{1/2} \cdot \rho \cdot V_{w}^{3} \cdot C}\; P}{V_{a}}$

Where ΔP_(T) is the change in total pressure between the upstream anddownstream sides of the rotor plane, ρ is the density of the fluid inthe stream, V_(w), is the free stream fluid speed V_(a) is theaccelerated velocity through the rotor, and CP is the coefficient ofpower.

A mixer ejector turbine (MET), as described herein, uses a mixer/ejectorpump in combination with highly cambered ringed airfoils to improveturbine efficiency. Two factors which may be important for optimal bladedesign for the MET system include the speed up of the flow at the rotorstation and/or the energy addition to the rotor wake flow in themixer/ejector. The one-dimensional control volume power predictions(above) account for and utilize both of these effects. The camberedshrouds and ejector bring more flow through the rotor allowing moreenergy extraction just due to higher flow rates. The mixer/ejectortransfers energy from the bypass flow to the rotor wake flow allowinghigher energy per unit mass flow rate through the rotor.

The higher velocities at the different radial positions along the blade(at different stations) can be taken advantage of through inductionfactor analyses in wind turbine blade design. Principles of both BET andmomentum conservation analysis may be applied to facilitate turbineblade design. Iterative empirical testing may be utilized as well.Results of tests conducted by the Inventors have shown that the energytransfer from the bypass flow occurs primarily in the lobe region of thewake flow with virtually no energy addition near the centerbody. Thus,by varying the blade power extraction (total pressure extractionprofile) with high power extraction per mass flow rate for the flow thatpasses through the lobes and mixes quickly with the bypass flow (e.g.,at the top ⅓ of the blade) and lower power extraction per flow rate forthe unmixed flow (e.g., toward the blade root) a greater amount of powermay be extracted. Further, without reducing the power extraction perunit flow rate at the blade root section, the center region of theejector flowfield would not be able to pass through the wake diffusionwithout stalling. In tests conducted, screens were used to optimizeradial power extraction profiles for the MET system.

A MET in accordance with one embodiment provides increased fluid flowvelocity at the perimeter region of the rotor plane relative to thefluid flow velocity at a center region of the rotor plane. An unevenlyloaded blade, as described herein, may be designed to accommodate moreenergy extraction per unit mass flow rate at the perimeter region andless energy extraction per unit mass flow rate at the center region ofthe rotor plane. Thus, an unevenly loaded blade, as described herein isbetter suited than a conventional symmetrically loaded blade to maximizepower extraction from fluid with a non-uniform flow velocity.

These and other non-limiting features or characteristics of the presentdisclosure will be further described below.

BRIEF DESCRIPTION OF THE DRAWINGS

The following is a brief description of the drawings, which arepresented for the purposes of illustrating the disclosure set forthherein and not for the purposes of limiting the same.

FIG. 1 is a front right perspective view of an example horizontal windturbine of the prior art.

FIG. 2 is a perspective view depicting delineated cross sections thatrepresent stations of one of the rotor blades of the turbine of FIG. 1.

FIG. 3 is an orthographic end view of the delineated cross sections thatrepresent each station of the rotor blade of FIG. 2.

FIG. 4 illustrates even blade loading of a power-extracting region ofthe rotor blade of FIGS. 2 and 3.

FIG. 5 is a graphical representation of the pressure differential perstation (blade loading) represented in FIG. 4.

FIG. 6 is a front perspective view of an exemplary turbine embodiment ofthe present disclosure.

FIG. 7 is a cross section of the turbine represented in FIG. 6.

FIG. 8 is a perspective view depicting delineated cross sections thatrepresent the stations of one of the rotor blades of the turbine ofFIGS. 6 and 7.

FIG. 9 is an orthographic end view of the delineated cross sections thatrepresent each station of the rotor blade of FIG. 8.

FIG. 10 illustrates uneven blade loading of the rotor blade of FIGS. 8and 9.

FIG. 11 is a graphical representation of the pressure differential perstation (blade loading) represented in FIG. 10.

FIGS. 12-14 are views of further exemplary shrouded turbine embodimentsof the present disclosure.

DETAILED DESCRIPTION

A more complete understanding of the components, processes, andapparatuses disclosed herein can be obtained by reference to theaccompanying figures. These figures are intended to demonstrate thepresent disclosure and are not intended to show relative sizes anddimensions or to limit the scope of the disclosed embodiment(s).

Although specific terms are used in the following description, theseterms are intended to refer only to particular structures in thedrawings and are not intended to limit the scope of the presentdisclosure. It is to be understood that like numeric designations referto components of like function.

A value modified by the term “about” or the term “substantially” shouldbe interpreted as disclosing both the stated value as well as a range ofvalues proximal to the stated value within the meaning dictated by thecontext and as would readily be understood by one of ordinary skill inthe art. For example, a value modified by the term “about” or the term“substantially” should be interpreted as disclosing a range of valuesproximal to the value accounting for at least the degree of errorrelated to the value, for example, based on design/manufacturetolerances and/or measurement errors affected the value.

Turbines may be used to extract energy from a variety of suitable fluidssuch as air (e.g., wind turbines) and water (e.g., hydro turbines),e.g., to generate electricity. In general, principles relating toturbine design and operation, such as described herein, remainconsistent regardless of fluid type. For example, the aerodynamicprinciples of a wind turbine also apply to hydrodynamic principles of awater turbine. Thus, while portions of the present disclosure may bedirected towards one or more example embodiments of turbines it will beappreciated by one of ordinary skill in the art that such teachings maybe universally applicable, for example, regardless of fluid type.

A Mixer-Ejector Turbine (MET) provides an improved means of extractingpower from flowing fluid. A primary shroud contains a rotor whichextracts power from a primary fluid stream. A mixer-ejector pump isincluded that ingests bypass for use in energizing the primary fluidflow. This mixer-ejector pump may promote turbulent mixing of theaforementioned two fluid streams. This mixing enhances the powerextraction from the MET system by increasing the amount of fluid flowthrough the system, increasing the velocity at the rotor plane for morepower availability, and reducing the pressure on down-wind side of therotor plane and energizing the rotor wake. As understood by one skilledin the art, the aerodynamic principles of a MET are not restricted to aspecific fluid, and may apply to any fluid, defined as any liquid, gasor combination thereof and therefore includes water as well as air. Inother words, the aerodynamic principles of a mixer ejector wind turbineapply to hydrodynamic principles in a mixer ejector water turbine.

Exemplary rotors, according to the present disclosure, may include aconventional propeller-like rotor, a rotor/stator assembly, amulti-segment propeller-like rotor, or any type of rotor understood byone skilled in the art. In an example embodiment, a rotor may beassociated with a turbine shroud, such as described herein, and mayinclude one or more rotor blades, for example, one or more unevenlyloaded rotor blades, such as described herein, attached to a rotationalshaft or hub. As used herein, the term “blade” is not intended to belimiting in scope and shall be deemed to include all aspects of suitableblades, including those having multiple associated blade segments.

The leading edge of a turbine blade and/or the leading edge of a turbineshroud may be considered the front of the turbine. The trailing edge ofa turbine blade and/or the trailing edge of an ejector shroud may beconsidered the rear of the turbine. A first component of the turbinelocated closer to the front of the turbine may be considered “upstream”of a second component located closer to the rear of the turbine. Putanother way, the second component is “downstream” of the firstcomponent.

In an example embodiment, the present disclosure relates to a turbinefor extracting power from a non-uniform flow velocity. In one exampleembodiment, the turbine may be configured for affecting the non-uniformflow velocity in the fluid (for example, the turbine may be a METincluding a turbine shroud that is in close proximity to or surrounds arotor and an ejector shroud that is in close proximity to or surroundsthe exit of the turbine shroud). More particularly, the presentdisclosure relates to the design and implementation (for example, in ashrouded turbine) of unevenly loaded rotor blade(s). In one exampleembodiment, the tip to hub variation in power extracted per mass flowrate is between 40% and 90%, or in other words, the area toward the tipregion of the rotor extracts between 40% and 90% more power per massflow rate than the area toward the root region at the hub of the rotorblade. Advantageously, the mass-average total pressure drop from theupstream area to the downstream area may remain the same.

FIG. 1 is a perspective view of an embodiment of a conventional HAWT 100of the prior art. The HAWT 100 includes rotor blades 112 that are joinedat a central hub 141 and rotate about a central axis 105. The hub isjoined to a shaft that is co-axial with the hub and with the nacelle150. The nacelle 150 houses electrical generation equipment (not shown).The rotor plane is represented by the dotted line 115.

Referring to FIGS. 2-4, an exemplary rotor blade 112, (e.g., for theHAWT 100 of FIG. 1) is shown. Cross sections 160, 162, 164 . . . 180 aredelineated at different radial positions relative to the axis ofrotation (e.g., relative to the central axis of FIG. 1) along a centralblade axis 107. Each cross section 160, 162, 164 . . . 180 represents astation along the blade 112 and defines an airfoil. According to theillustrated embodiment, each airfoil may be characterized based on thelength and pitch of a cord between the leading and trailing edges of theairfoil (note this is merely an illustrative embodiment, however, andany number of parameters relating to the shape and/or pitch of theairfoil may be identified and used to characterize the airfoil). Crosssection 160 defines chord 161. Similarly, cross section 180 defineschord 181. Referring to FIG. 3, each chord has a length and a pitch asseen in the length and relative pitch angle between chords 161 and 181.The chord length and pitch of each cross section affects the loading onthe blade at the corresponding station. FIG. 4, depicts blade loading(Δp) across different regions of the blade 112. Blade loading (Δp) isillustrated using horizontal hash markings wherein the spacing betweenthe hash markings is inversely proportional to blade loading. Asdepicted in FIG. 4, conventional HAWT blades are designed to have evenblade loading at each station across a power-extracting region of theblade 112 when operating in a fluid stream. Note that the blade 112includes two non-power-extracting regions proximal to the root and tipof the blade (see cross sections 160 and 180, respectively). Thenon-power extracting regions are identifiable by the sudden minimalblade loading represented in FIG. 4 by sparse horizontal hash marking atthe root and tip of the blade 112.

FIG. 5 depicts a graphical representation of blade loading per stationas represented in FIG. 4 for blade 112. As noted with respect to FIG. 5even blade loading is evident for stations in a power-extracting regionof the blade 112 (see, e.g., cross sections 162, 164, 166 and 178).Minimal blade loading is evident for stations in non-energy extractingregions of the blade 112 near the root and tip (see, e.g.,cross-sections 160 and 180, respectively). The position of the crosssections 160, 162, 164 . . . 180 along the axis 107 is represented alongthe vertical axis of the graph. Blade loading, characterized by apressure differential (Δp) in pounds per square foot (psf) isrepresented along the horizontal axis of the graph. The verticalalignment cross sections from the power-extracting region of the blade112 represents substantially identical, or even, blade loading.

FIG. 6 is a perspective view of an exemplary embodiment of a shroudedturbine 200 of the present disclosure. FIG. 7 is a cross-sectional viewof the shrouded turbine of FIG. 6. Referring to FIG. 6, the shroudedturbine 200 includes a turbine shroud 210, a nacelle body 250, a rotor239, and an ejector shroud 220. The turbine shroud 210 includes a frontend 212, also known as an inlet end or a leading edge. The turbineshroud 210 also includes a rear end 216, also known as an exhaust end ortrailing edge. The ejector shroud 220 includes a front end, inlet end orleading edge 222, and a rear end, exhaust end, or trailing edge 224.Support members 206 are shown connecting the turbine shroud 210 to theejector shroud 220.

The rotor 239 is operatively coupled to the nacelle body 250. The rotor239 includes a central hub 241 at the proximal end of one or more rotorblades 240 and defines a rotor plane where the fluid flow intersects theblades 240. The central hub 241 is rotationally engaged with the nacellebody 250. The nacelle body 250 and the turbine shroud 210 are supportedby a tower 202. In the present embodiment, the rotor 239, turbine shroud210, and ejector shroud 220 are coaxial with each other, i.e. they sharea common central axis 205.

Referring to FIG. 7. The turbine shroud 210 has the cross-sectionalshape of an airfoil with a leading edge 212 and the suction side (i.e.low pressure side) on the interior of the shroud. The rear end 216 ofthe turbine shroud also has mixing lobes including rotor flow (lowenergy) mixing lobes 215 and bypass flow (high energy) mixing lobes 217.The mixing lobes extend downstream beyond the rotor blades 240. Putanother way, the trailing edge 216 of the turbine shroud is shaped toform two different sets of mixing lobes. High energy mixing lobes 217extend inwardly towards the central axis 205 of the mixer shroud. Lowenergy mixing lobes 215 extend outwardly away from the central axis 205.An opening in the sidewall 219 between the low energy lobe 215 and thehigh energy mixing lobe 217 increases mixing between high and low energystreams.

A mixer-ejector pump is formed by the ejector shroud 220 in fluidcommunication with the ring of high energy mixing lobes 217 and lowenergy mixing lobes 215 on the turbine shroud 210. The mixing lobes 217extend downstream toward the inlet end 222 of the ejector shroud 220.This mixer-ejector pump provides the means for increased operationalefficiency. The area of higher velocity fluid flow is generally depictedby the shaded area 245 (FIG. 7). In accordance with the presentdisclosure, rotor blades in a mixer-ejector turbine may be designedappropriately to take advantage of the energy transfer as a result ofthe mixing between the bypass flow and the rotor wake flow. This mixingis strongly determined by the height and shape of the lobes 217.

Referring to FIG. 8-10, an example rotor blade 240 (e.g., for themixer-ejector turbine 200 of FIGS. 6-7), is shown. The blade 240,advantageously includes a power-extracting region adapted forradially-varied (relative to the axis of rotation) power extraction permass flow rate. Cross sections 260, 262, 264 . . . 284 are delineated atdifferent radial positions relative to the axis of rotation (e.g.,relative to axis 205 of FIGS. 6-7) along the central axis 207 of theblade. Each cross section 260, 262, 264, . . . , 284 represents astation along the blade 240 and defines an airfoil. According to theillustrated embodiment, each airfoil may be characterized based on thelength and pitch of a cord between the leading and trailing edges of theairfoil (note this is merely an illustrative embodiment, however, andany number of parameters relating to the shape and/or pitch of theairfoil may be identified and used to characterize the airfoil). Crosssection 260 defines chord 261. Similarly, cross section 284 defineschord 283.

In one example embodiment, the rotor blade 240 may be constructed and/ormodeled using multiple blade segments, e.g., such as defined betweencross sections, wherein each blade segment actually has or is assumed tohave a constant airfoil shape and pitch (e.g., a constant chord lengthand chord pitch). In this embodiment, the airfoil shape and/or pitch ofone segment need not be contiguous with the airfoil shape and/or pitchof an adjacent segment. In another example embodiment, the rotor blade240 may be constructed and/or modeled as a contiguous structure, e.g.,wherein the shape and pitch of the airfoil changes contiguously withrespect to radial-position. Thus, for example, the rotor blade 240 maybe modeled as an infinite number of blade segments of a width (dr)approaching zero. Analysis of forces and/or structural parameters can beachieved by integrating over a length of the blade 240 (0 to R).

Referring to FIG. 9, each chord has a length and a pitch as seen in thelength and relative pitch angle between chords 261 and 283. Airfoilcharacteristics, such as the chord length and pitch of each crosssection affect the loading on the blade at the corresponding station.Thus, for blade 240, the pitch and/or shape of the airfoil at a firstcross section, e.g., cross section 284, is configured, so that the powerextraction per mass flow rate of the blade 240 at that first crosssection is different than the power extraction per mass flow rate of theblade 240 at a second cross section, e.g., cross section 260. Blade 240is advantageously configured to take advantage of the non-uniform flowprofile resulting from the mixer-ejector pump of the turbine 200 ofFIGS. 6-7 with greater loading toward the tip to take advantage of theregion of greater fluid flow velocity (shaded area 245 of FIG. 7). Blade240 illustrates how a power-extracting region of an unevenly loadedblade may optimized for an expected relative flow velocity between fluidflow at a first radial position and fluid flow at a second radialposition. In example embodiments, the power-extracting region of anunevenly loaded blade may optimized based on optimal lift/drag ratiosfor each radial position such as a maximal lift/drag ratio prior tostall or prior to a selected safety threshold. As illustrated by blade240, the greater the relative flow velocity at a radial position, thegreater the optimal lift/drag ratio at that position and the greater thepower extraction per mass flow rate at that position. In an exampleembodiment, relative flow velocity between two radial positions may berelated, for example, proportional to relative power extraction per massflow rate between the two radial positions.

FIG. 10, depicts blade loading (Δp) across different regions of theblade 240. Blade loading (Δp) is illustrated using horizontal hashmarkings wherein the spacing between the hash markings is inverselyproportional to blade loading. As depicted in FIG. 10, blade 240 isdesigned to have uneven blade loading at each station across apower-extracting region of the blade 240 when operating in the fluidstream of turbine 200 of FIGS. 6-7. More particularly, blade 240 isconfigured to exhibit greater loading toward the tip to take advantageof the region of greater fluid flow velocity. Note that for theembodiment depicted in FIG. 4 the power-extracting region includesportions of the blade from cross section 260 to cross section 284, e.g.,there are no non-power extracting regions toward the tip or root.

FIG. 11 depicts a graphical representation of blade loading per stationas represented in FIG. 10 for blade 240. As noted with respect to FIG.10 uneven blade loading is evident for stations of the blade 240 (see,e.g., the gradual decrease in blade loading from station 284 to station260). The position of cross-sections 260, 262, 264 . . . 284 along thecentral blade axis 207 is represented along the vertical axis of thegraph. Blade loading, characterized by a pressure differential (Δp) inpounds per square foot (psf) is represented along the horizontal axis ofthe graph. In some embodiments, the load at a station that representsthe blade tip (cross section 284) is between 20% and 45% greater thanthe load at a mean section (cross section 270), similarly, the load at astation that represents the blade root (cross section 260) is 20% to 45%lower than that of the mean section (cross section 270).

It is noted that mixer/ejector turbine 200 of FIGS. 6-7 is only oneexample of a shrouded turbine which may be used in accordance with theapparatus, systems and methods of the present disclosure to produce anon-uniform flow profile across a rotor plane. Indeed, otherimplementations of shrouded turbines, e.g., with or without an ejectorshroud and/or with or without mixing lobes may also be used instead toproduce non-uniform flow profile across a rotor plane. See, for example,FIGS. 12-14, depicting further exemplary shrouded turbine embodimentscapable of producing a non-uniform flow profile across a rotor plane.

FIG. 12 is a perspective view of a further example embodiment of ashrouded turbine 300 including a turbine shroud 310 characterized by aringed airfoil. Unlike the turbine 200 of FIGS. 6-7, turbine 300 doesnot include an ejector shroud. Turbine 300 also includes a nacelle body350 and a rotor 339 including a plurality of rotor blades 340. Unlikethe turbine 200 of FIGS. 6-7, turbine 300 in the embodiment of FIG. 12does not include an ejector shroud. The turbine shroud 310advantageously induces a non-uniform flow profile across a rotor plane.Turbine shroud 310 further includes mixing elements 315 and 317. Mixingelements 315 and 317 include inward turning mixing elements 317 whichturn inward toward a central axis 305 and outward turning mixingelements 315 which turn outward from the central axis 305. The turbineshroud 310 includes a front end 312 also known as an inlet end or aleading edge. Mixing elements 315 and 317 include a rear end 316, alsoknown as an exhaust end or trailing edge. Support structures 306 areengaged at the proximal end, with the nacelle body 350 and at the distalend with the turbine shroud 310. The rotor, nacelle body 350, andturbine shroud 310 are concentric about a common axis 305 (which is theaxis of rotation for the rotor 339) and are supported by a towerstructure 302.

FIG. 13 depicts a cross-sectional view of a further example embodimentof a shrouded turbine 400. Turbine 400 includes a shrouded turbine 410characterized by a ringed airfoil. Turbine 400 also includes a nacellebody 450 and a rotor 439 including a plurality of rotor blades 440.Similar to the turbine 300 of FIG. 12, the turbine 400 depicted in FIG.13 does not include an ejector shroud. The turbine shroud 410advantageously induces a non-uniform flow profile across a rotor plane409. Unlike the turbine shroud 310 in FIG. 12, the turbine shroud 410 inthe embodiment of FIG. 13, does not include mixing elements. The turbineshroud 410 includes a front end 412 also known as an inlet end or aleading edge and a rear end 416, also known as an exhaust end ortrailing edge. Support structures 406 are engaged at a proximal end withthe nacelle body 450 and at the distal end with the turbine shroud 410.The rotor 439, nacelle body 450, and turbine shroud 410 are concentricabout a common axis 405 (which is the axis of rotation for the rotor439) and are supported by a tower structure 402.

FIG. 14 depicts a cross section view of a further example embodiment ofa shrouded turbine 500. Turbine 500 includes a shrouded turbine 510characterized by a ringed airfoil. Turbine 500 also includes a nacellebody 550 and a rotor 539 including a plurality of rotor blades 540.Similar to the turbines 300 and 400 of FIGS. 12-13, the turbine 500depicted in FIG. 14 does not include an ejector shroud. The turbineshroud 510 advantageously induces a non-uniform flow profile across arotor plane 509. Instead of including mixing lobes, turbine shroud 510advantageously defines a plurality of passages 519 extending from theouter surface to the inner surface of the turbine shroud 510. Passages519 act as bypass ducts that providing mixing between a bypass flow 503and the fluid flow through the turbine 500 down-stream from the rotorplane 509 thus introducing a volume of high energy flow to the exitflow. The turbine shroud 510 includes a front end 512 also known as aninlet end or a leading edge and a rear end 516, also known as an exhaustend or trailing edge. Support structures 506 are engaged at a proximalend with the nacelle body 550 and at the distal end with the turbineshroud 510. The rotor 539, nacelle body 550, and turbine shroud 510 areconcentric about a common axis 505 (which is the axis of rotation forthe rotor) and are supported by a tower structure 502.

It is contemplated that a turbine shroud may not be the only mechanismin a turbine for inducing a non-uniform flow profile across a rotorplane of a turbine. Indeed, any appropriate mechanism may be used tomanipulate fluid flow instead of or in addition to a turbine shroud.

The present disclosure has been described with reference to exemplaryembodiments. Obviously, modifications and alterations will occur toothers upon reading and understanding the preceding detaileddescription. It is intended that the present disclosure be construed asincluding all such modifications and alterations insofar as they comewithin the scope of the appended claims or the equivalents thereof.

1. A shrouded axial flow fluid turbine comprising: an aerodynamicallycontoured turbine shroud having an inlet and configured to produce anon-uniform fluid velocity profile across a rotor plane when exposed toa fluid flow; and a rotor disposed downstream of the inlet andconfigured to extract energy from fluid passing through the rotor plane,the rotor comprising: a central hub; and a plurality of blades, eachblade including: a root region having a blade root; a tip region havinga blade tip; a mid-region disposed between the root region and the tipregion; and a blade axis extending radially from the blade root to theblade tip; each blade configured to have a value of power extraction permass flow rate at a radial position along the blade axis that is greaterat a first radius in the tip region of the blade than at second radiusin the mid-region of the blade when exposed to the non-uniform fluidvelocity profile.
 2. The shrouded axial flow fluid turbine of claim 1,wherein an average value of power extraction per mass flow rate forradial positions along the blade axis in the tip region is larger thanan average value of power extraction per mass flow rate for radialpositions along the blade axis in the mid-region when exposed to thenon-uniform fluid velocity profile.
 3. The shrouded axial flow fluidturbine of claim 1, wherein an average value of power extraction permass flow rate for radial positions along the blade axis in themid-region is larger than an average value of power extraction per massflow rate for radial positions along the blade axis in the root regionwhen exposed to the non-uniform fluid velocity profile.
 4. The shroudedaxial flow fluid turbine of claim 1, wherein each blade is configured tohave a value of power extraction per mass flow rate at a radial positionalong the blade axis that varies as a function of distance of the radialposition from a central axis of rotation of the rotor when exposed tothe non-uniform fluid velocity profile.
 5. The shrouded axial flow fluidturbine of claim 1, wherein a pitch, a chord length and a camber of eachblade at each radial position along the blade axis are configured toproduce a non-uniform power extraction per mass flow rate profile alongthe blade axis.
 6. The shrouded axial flow fluid turbine of claim 1,wherein, for each blade, an average value of power extraction per massflow rate for radial positions along the blade axis in the tip region isbetween 20% and 45% greater than an average value of power extractionper mass flow rate for radial positions along the blade axis from theblade root to the blade tip.
 7. The shrouded axial flow fluid turbine ofclaim 1, wherein, for each blade, an average value of power extractionper mass flow rate for radial positions along the blade axis in the rootregion is between 20% and 45% less than an average value of powerextraction per mass flow rate for radial positions along the blade axisfrom the blade root to the blade tip.
 8. The shrouded axial flow fluidturbine of claim 1, wherein the turbine shroud further comprises one ormore mixing devices disposed downstream of the rotor and extendingdownstream.
 9. The axial flow fluid turbine of claim 10, wherein the oneor more mixing devices comprise mixer lobes.
 10. The axial flow fluidturbine of claim 10, further comprising an ejector shroud downstream ofthe turbine shroud.
 11. The axial flow fluid turbine of claim 12,wherein turbine shroud with one or more mixing devices and the ejectorshroud form a mixer-ejector pump, and the wherein the non-uniform flowvelocity profile at the rotor plane is created, in part, by themixer-ejector pump.
 12. The axial flow fluid turbine of claim 10,wherein the mixing devices function as flow straighteners to straightena fluid flow downstream of the rotor.
 13. A rotor blade coupleable to arotor of a shrouded fluid turbine having a turbine shroud that producesa non-uniform fluid velocity profile across a rotor plane when exposedto a fluid flow, the rotor including a central hub configured to receiveone or more rotor blades, the rotor blade comprising: a root regionhaving a blade root; a tip region having a blade tip; a mid-regiondisposed between the root region and the tip region; and a blade axisextending from the blade root to the blade tip; wherein the blade isconfigured to, when connected with the central hub, have a value ofpower extraction per mass flow rate at a radial position along the bladeaxis that is greater at a first radius in the tip region of the bladethan at a second radius in the mid-region of the blade when exposed tothe non-uniform fluid velocity profile.
 14. The rotor blade of claim 13,wherein a pitch of the blade as a function of radial position along theblade axis is configured to, when connected with the central hub,produces an average value of power extraction per mass flow rate forradial positions along the blade axis in the tip region greater than anaverage value of power extraction per mass flow rate for radialpositions along the blade axis in the mid-region when exposed to thenon-uniform fluid velocity profile.
 15. The rotor blade of claim 13,wherein a pitch of the blade as a function of radial position along theblade axis is configured to, when connected with the central hub,produce a negative average value of power extraction per mass flow rateor radial positions along the blade axis in the root region when exposedto the non-uniform fluid velocity profile.
 16. A rotor configured foruse with a shrouded fluid turbine having a turbine shroud that creates anon-uniform fluid velocity profile across a rotor plane when exposed toa fluid flow, the rotor comprising: a central hub with a central axis ofrotation; one or more rotor blades, each of the one or more rotor bladescomprising: a root region having a blade root that couples with thecentral hub; a tip region having a blade tip; a mid-region disposedbetween the root region and the tip region; and a blade axis extendingfrom the blade root to the blade tip; wherein, for each of the one ormore rotor blades, a pitch of the blade as a function of radial positionalong the blade axis is configured to, when connected with the centralhub, produce a power extraction per mass flow rate that is greater at afirst radius in the tip region of the blade than at second radius in themid-region of the blade when exposed to the non-uniform fluid velocityprofile.
 17. A method of operating a shrouded axial flow fluid turbineincluding an aerodynamically contoured turbine shroud having an inlet,and a rotor disposed downstream of the turbine shroud inlet, the rotorincluding a plurality of blades, each blade having a root regionincluding a blade root, a tip region including a blade tip, and amid-region disposed between the root region and the tip region, themethod comprising: establishing a non-uniform fluid flow through a rotorplane in which an average velocity of fluid flowing through an area ofthe rotor plane associated with the tip region of each blade is greaterthan an average velocity of fluid flowing through an area of the rotorplane associated with the mid-region of each blade; and extracting powerfrom the non-uniform fluid flow using the plurality of blades byextracting a greater average power per mass flow rate over the tipregion of each blade than an average power per mass flow rate extractedover the a mid-region of each blade.
 18. The method of claim 17, whereinthe rotor has an axis of rotation, and wherein each blade has a value ofpower extraction per unit mass flow rate at a radial position along ablade axis that varies as a function of the distance of the radialposition from the rotor axis of rotation when exposed to the non-uniformfluid velocity profile.
 19. The method of claim 17, wherein, for eachblade, an average value of power extraction per mass flow rate forradial positions along the blade axis in the tip region is between 20%and 45% greater than an average value of power extraction per mass flowrate for radial positions along the blade axis from the blade root tothe blade tip.
 20. The method of claim 17, wherein the turbine shroudfurther includes one or more mixing devices disposed downstream of therotor and extending downstream.
 21. The method of claim 20, wherein theone or more mixing devices comprise mixer lobes.
 22. The method ofclaims 20, wherein the axial flow fluid turbine further includes anejector shroud downstream of the turbine shroud.
 23. The method of claim21, wherein turbine shroud with mixing devices and the ejector shroudform a mixer-ejector pump, and the wherein the non-uniform flow velocityprofile at the rotor plane is created, in part, by the mixer-ejectorpump.
 24. The method of claim 20, wherein the mixing devices function asflow straighteners to straighten a fluid flow downstream of the rotor.25. The method of claim 17, wherein the shrouded axial flow turbinegenerates electricity from the power extracted from the non-uniformfluid flow by the rotor.
 26. A turbine comprising a rotor that (i) isconfigured to extract energy from a fluid flow characterized by aturbine-induced non-uniform fluid velocity profile across a rotor planeand (ii) includes at least one unevenly-loaded rotor blade having apower-extracting region in which power extraction per mass flow rate ata first radial position relative to an axis of rotation is differentthan power extraction per mass flow rate at a second radial positionrelative to the axis of rotation.
 27. The turbine of claim 26, whereinan airfoil of the blade at each of the first and second radial positionsis configured based on a pitch or a shape of the airfoil to affect thedifference between power extraction per mass flow rate at the firstradial position and power extraction per mass flow rate at the secondradial position.
 28. The turbine of claim 26, wherein theturbine-induced non-uniform velocity profile is characterized by agreater flow velocity at the first radial position than at the secondradial position and wherein power extraction per mass flow rate at thefirst radial position is greater than power extraction per mass flowrate at the second radial position.
 29. A method for manufacturing anunevenly-loaded rotor blade, the method comprising: identifying along apower extracting region of the blade a first radial position relative toan axis of rotation of the blade having an expected exposure to agreater flow velocity than a second radial position relative to the axisof rotation along the power extracting region of the blade; andconfiguring the power-extracting region to affect greater powerextraction per mass flow rate at the first axial position than at thesecond axial position.